Hey again,
In my task , after this question, I need to calculate a few limits using the formula

I managed to calculate all the limits in the task except of this limit

I tried many times but I couldn't write this expression as a sum of f(k/n)...
The problem is what's inside the ln function , i.e 2n+1 , 2n+2 , ... , 2n+k , can't be written as an expression of k/n , so I am kinda stuck....